Let the parabola y = x² + px – 3, meet the coordinate axes at the points P, Q and R. If the circle C with centre at (–1, –1) passes through the points P, Q and R, then the area of $∆$PQR is

y = x² + px – 3

Let $\mathrm{P}(\alpha ,0),\mathrm{Q}(\beta ,0),\mathrm{R}(0,-3)$

Circle with centre (-1, -1) is $(x+1{)}^2+(y+1{)}^2=r^2$

Passes through (0, -3)

$1^2+{\left(-2\right)}^2=r^2$

$(x+1{)}^2+(y+1{)}^2=5$

Put y=0

$\begin{array}{r}(x+1{)}^2=5-1\end{array}$

$\begin{array}{r}(x+1{)}^2=4\end{array}$

$x+1=\pm 2$

x=1 or x=-3

P(1, 0) and Q(-3, 0)

Area of $\mathrm{\Delta PQR}=\frac{1}{2}\left|\begin{array}{ccc}1& 0& 1\\ -3& 0& 1\\ 0& -3& 1\end{array}\right|=6$